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(12-2x)2=144-4x^2+48x
We move all terms to the left:
(12-2x)2-(144-4x^2+48x)=0
We add all the numbers together, and all the variables
-(144-4x^2+48x)+(-2x+12)2=0
We multiply parentheses
-(144-4x^2+48x)-4x+24=0
We get rid of parentheses
4x^2-48x-4x-144+24=0
We add all the numbers together, and all the variables
4x^2-52x-120=0
a = 4; b = -52; c = -120;
Δ = b2-4ac
Δ = -522-4·4·(-120)
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{4624}=68$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-68}{2*4}=\frac{-16}{8} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+68}{2*4}=\frac{120}{8} =15 $
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